LMFDB - Embedded newform 196.2.j.a.111.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.25
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.25

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38475 - 0.287182i) q^{2} +(1.31156 + 1.64465i) q^{3} +(1.83505 - 0.795349i) q^{4} +(-2.15171 + 1.71594i) q^{5} +(2.28850 + 1.90077i) q^{6} +(-0.0757418 - 2.64467i) q^{7} +(2.31268 - 1.62835i) q^{8} +(-0.317107 + 1.38934i) q^{9} +O(q^{10})$	\(q+(1.38475 - 0.287182i) q^{2} +(1.31156 + 1.64465i) q^{3} +(1.83505 - 0.795349i) q^{4} +(-2.15171 + 1.71594i) q^{5} +(2.28850 + 1.90077i) q^{6} +(-0.0757418 - 2.64467i) q^{7} +(2.31268 - 1.62835i) q^{8} +(-0.317107 + 1.38934i) q^{9} +(-2.48680 + 2.99407i) q^{10} +(-5.04250 + 1.15092i) q^{11} +(3.71486 + 1.97487i) q^{12} +(4.41417 - 1.00751i) q^{13} +(-0.864384 - 3.64045i) q^{14} +(-5.64422 - 1.28826i) q^{15} +(2.73484 - 2.91902i) q^{16} +(-1.55736 + 3.23389i) q^{17} +(-0.0401206 + 2.01495i) q^{18} -1.68938 q^{19} +(-2.58374 + 4.86020i) q^{20} +(4.25021 - 3.59322i) q^{21} +(-6.65207 + 3.04185i) q^{22} +(-3.00519 - 6.24035i) q^{23} +(5.71129 + 1.66785i) q^{24} +(0.572838 - 2.50977i) q^{25} +(5.82318 - 2.66281i) q^{26} +(2.98492 - 1.43746i) q^{27} +(-2.24242 - 4.79286i) q^{28} +(-2.62766 - 1.26542i) q^{29} +(-8.18578 - 0.162991i) q^{30} -2.18485 q^{31} +(2.94877 - 4.82750i) q^{32} +(-8.50641 - 6.78364i) q^{33} +(-1.22783 + 4.92536i) q^{34} +(4.70105 + 5.56060i) q^{35} +(0.523100 + 2.80172i) q^{36} +(9.60088 + 4.62354i) q^{37} +(-2.33936 + 0.485158i) q^{38} +(7.44646 + 5.93835i) q^{39} +(-2.18207 + 7.47215i) q^{40} +(-2.45112 + 1.95471i) q^{41} +(4.85356 - 6.19628i) q^{42} +(-0.804546 - 0.641604i) q^{43} +(-8.33787 + 6.12254i) q^{44} +(-1.70169 - 3.53359i) q^{45} +(-5.95355 - 7.77827i) q^{46} +(0.583958 + 2.55849i) q^{47} +(8.38767 + 0.669372i) q^{48} +(-6.98853 + 0.400624i) q^{49} +(0.0724760 - 3.63990i) q^{50} +(-7.36118 + 1.68014i) q^{51} +(7.29892 - 5.35964i) q^{52} +(3.85172 - 1.85489i) q^{53} +(3.72054 - 2.84773i) q^{54} +(8.87512 - 11.1290i) q^{55} +(-4.48162 - 5.99292i) q^{56} +(-2.21572 - 2.77843i) q^{57} +(-4.00205 - 0.997664i) q^{58} +(-1.51285 + 1.89706i) q^{59} +(-11.3821 + 2.12511i) q^{60} +(-5.08482 + 10.5587i) q^{61} +(-3.02547 + 0.627450i) q^{62} +(3.69835 + 0.733411i) q^{63} +(2.69693 - 7.53170i) q^{64} +(-7.76922 + 9.74230i) q^{65} +(-13.7274 - 6.95074i) q^{66} +13.2842i q^{67} +(-0.285764 + 7.17300i) q^{68} +(6.32167 - 13.1271i) q^{69} +(8.10668 + 6.34997i) q^{70} +(1.49968 + 3.11413i) q^{71} +(1.52896 + 3.72944i) q^{72} +(-8.97767 - 2.04910i) q^{73} +(14.6226 + 3.64524i) q^{74} +(4.87900 - 2.34960i) q^{75} +(-3.10009 + 1.34364i) q^{76} +(3.42572 + 13.2486i) q^{77} +(12.0169 + 6.08463i) q^{78} -4.00244i q^{79} +(-0.875748 + 10.9737i) q^{80} +(10.1308 + 4.87876i) q^{81} +(-2.83283 + 3.41069i) q^{82} +(0.261589 - 1.14609i) q^{83} +(4.94149 - 9.97414i) q^{84} +(-2.19815 - 9.63073i) q^{85} +(-1.29835 - 0.657409i) q^{86} +(-1.36518 - 5.98125i) q^{87} +(-9.78756 + 10.8727i) q^{88} +(12.0984 + 2.76138i) q^{89} +(-3.37119 - 4.40444i) q^{90} +(-2.99886 - 11.5977i) q^{91} +(-10.4779 - 9.06119i) q^{92} +(-2.86557 - 3.59331i) q^{93} +(1.54339 + 3.37516i) q^{94} +(3.63505 - 2.89886i) q^{95} +(11.8070 - 1.48188i) q^{96} +2.97945i q^{97} +(-9.56229 + 2.56174i) q^{98} -7.37069i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.38475	−	0.287182i	0.979165	−	0.203068i
$2$	1.38475	−	0.287182i	0.979165	−	0.203068i
$3$	1.31156	+	1.64465i	0.757231	+	0.949538i	0.999788	−	0.0205993i	$-0.00655742\pi$
$3$	1.31156	+	1.64465i	0.757231	+	0.949538i	−0.242557	+	0.970137i	$0.577986\pi$
$4$	1.83505	−	0.795349i	0.917526	−	0.397675i
$5$	−2.15171	+	1.71594i	−0.962276	+	0.767390i	−0.972583	−	0.232557i	$-0.925291\pi$
$5$	−2.15171	+	1.71594i	−0.962276	+	0.767390i	0.0103065	+	0.999947i	$0.496719\pi$
$6$	2.28850	+	1.90077i	0.934275	+	0.775984i
$7$	−0.0757418	−	2.64467i	−0.0286277	−	0.999590i
$7$	−0.0757418	−	2.64467i	−0.0286277	−	0.999590i
$8$	2.31268	−	1.62835i	0.817654	−	0.575710i
$9$	−0.317107	+	1.38934i	−0.105702	+	0.463112i
$10$	−2.48680	+	2.99407i	−0.786394	+	0.946809i
$11$	−5.04250	+	1.15092i	−1.52037	+	0.347015i	−0.899508	−	0.436904i	$-0.856075\pi$
$11$	−5.04250	+	1.15092i	−1.52037	+	0.347015i	−0.620863	+	0.783919i	$0.713218\pi$
$12$	3.71486	+	1.97487i	1.07239	+	0.570094i
$13$	4.41417	−	1.00751i	1.22427	−	0.279432i	0.438945	−	0.898514i	$-0.355352\pi$
$13$	4.41417	−	1.00751i	1.22427	−	0.279432i	0.785326	+	0.619082i	$0.212495\pi$
$14$	−0.864384	−	3.64045i	−0.231016	−	0.972950i
$15$	−5.64422	−	1.28826i	−1.45733	−	0.332626i
$16$	2.73484	−	2.91902i	0.683710	−	0.729754i
$17$	−1.55736	+	3.23389i	−0.377715	+	0.784333i	0.622284	+	0.782792i	$0.286205\pi$
$17$	−1.55736	+	3.23389i	−0.377715	+	0.784333i	−0.999999	+	0.00154143i	$0.999509\pi$
$18$	−0.0401206	+	2.01495i	−0.00945653	+	0.474928i
$19$	−1.68938			−0.387569			−0.193785	−	0.981044i	$-0.562076\pi$
$19$	−1.68938			−0.387569			−0.193785	+	0.981044i	$0.562076\pi$
$20$	−2.58374	+	4.86020i	−0.577742	+	1.08677i
$21$	4.25021	−	3.59322i	0.927471	−	0.784104i
$22$	−6.65207	+	3.04185i	−1.41823	+	0.648524i
$23$	−3.00519	−	6.24035i	−0.626626	−	1.30120i	−0.936581	−	0.350451i	$-0.886028\pi$
$23$	−3.00519	−	6.24035i	−0.626626	−	1.30120i	0.309955	−	0.950751i	$-0.399686\pi$
$24$	5.71129	+	1.66785i	1.16581	+	0.340448i
$25$	0.572838	−	2.50977i	0.114568	−	0.501954i
$26$	5.82318	−	2.66281i	1.14202	−	0.522221i
$27$	2.98492	−	1.43746i	0.574448	−	0.276639i
$28$	−2.24242	−	4.79286i	−0.423778	−	0.905766i
$29$	−2.62766	−	1.26542i	−0.487945	−	0.234982i	0.173701	−	0.984798i	$-0.444427\pi$
$29$	−2.62766	−	1.26542i	−0.487945	−	0.234982i	−0.661646	+	0.749817i	$0.730142\pi$
$30$	−8.18578	−	0.162991i	−1.49451	−	0.0297580i
$31$	−2.18485			−0.392410			−0.196205	−	0.980563i	$-0.562862\pi$
$31$	−2.18485			−0.392410			−0.196205	+	0.980563i	$0.562862\pi$
$32$	2.94877	−	4.82750i	0.521274	−	0.853389i
$33$	−8.50641	−	6.78364i	−1.48078	−	1.18088i
$34$	−1.22783	+	4.92536i	−0.210572	+	0.844693i
$35$	4.70105	+	5.56060i	0.794623	+	0.939913i
$36$	0.523100	+	2.80172i	0.0871833	+	0.466953i
$37$	9.60088	+	4.62354i	1.57837	+	0.760105i	0.998508	−	0.0546059i	$-0.0173902\pi$
$37$	9.60088	+	4.62354i	1.57837	+	0.760105i	0.579867	+	0.814711i	$0.303105\pi$
$38$	−2.33936	+	0.485158i	−0.379494	+	0.0787031i
$39$	7.44646	+	5.93835i	1.19239	+	0.950897i
$40$	−2.18207	+	7.47215i	−0.345016	+	1.18145i
$41$	−2.45112	+	1.95471i	−0.382801	+	0.305274i	−0.795918	−	0.605404i	$-0.793012\pi$
$41$	−2.45112	+	1.95471i	−0.382801	+	0.305274i	0.413117	+	0.910678i	$0.364440\pi$
$42$	4.85356	−	6.19628i	0.748920	−	0.956107i
$43$	−0.804546	−	0.641604i	−0.122692	−	0.0978437i	0.560221	−	0.828343i	$-0.310716\pi$
$43$	−0.804546	−	0.641604i	−0.122692	−	0.0978437i	−0.682914	+	0.730499i	$0.739287\pi$
$44$	−8.33787	+	6.12254i	−1.25698	+	0.923008i
$45$	−1.70169	−	3.53359i	−0.253672	−	0.526756i
$46$	−5.95355	−	7.77827i	−0.877803	−	1.14684i
$47$	0.583958	+	2.55849i	0.0851790	+	0.373194i	0.999494	−	0.0318104i	$-0.0101273\pi$
$47$	0.583958	+	2.55849i	0.0851790	+	0.373194i	−0.914315	+	0.405004i	$0.867270\pi$
$48$	8.38767	+	0.669372i	1.21066	+	0.0966155i
$49$	−6.98853	+	0.400624i	−0.998361	+	0.0572319i
$50$	0.0724760	−	3.63990i	0.0102497	−	0.514760i
$51$	−7.36118	+	1.68014i	−1.03077	+	0.235267i
$52$	7.29892	−	5.35964i	1.01218	−	0.743248i
$53$	3.85172	−	1.85489i	0.529074	−	0.254789i	−0.150223	−	0.988652i	$-0.547999\pi$
$53$	3.85172	−	1.85489i	0.529074	−	0.254789i	0.679297	+	0.733864i	$0.262285\pi$
$54$	3.72054	−	2.84773i	0.506302	−	0.387528i
$55$	8.87512	−	11.1290i	1.19672	−	1.50064i
$56$	−4.48162	−	5.99292i	−0.598881	−	0.800838i
$57$	−2.21572	−	2.77843i	−0.293480	−	0.368012i
$58$	−4.00205	−	0.997664i	−0.525495	−	0.131000i
$59$	−1.51285	+	1.89706i	−0.196957	+	0.246976i	−0.870496	−	0.492176i	$-0.836202\pi$
$59$	−1.51285	+	1.89706i	−0.196957	+	0.246976i	0.673539	+	0.739151i	$0.264773\pi$
$60$	−11.3821	+	2.12511i	−1.46942	+	0.274350i
$61$	−5.08482	+	10.5587i	−0.651045	+	1.35191i	0.270154	+	0.962817i	$0.412925\pi$
$61$	−5.08482	+	10.5587i	−0.651045	+	1.35191i	−0.921199	+	0.389092i	$0.872789\pi$
$62$	−3.02547	+	0.627450i	−0.384234	+	0.0796862i
$63$	3.69835	+	0.733411i	0.465948	+	0.0924011i
$64$	2.69693	−	7.53170i	0.337117	−	0.941463i
$65$	−7.76922	+	9.74230i	−0.963654	+	1.20838i
$66$	−13.7274	−	6.95074i	−1.68972	−	0.855577i
$67$			13.2842i			1.62293i	0.584403	+	0.811464i	$0.301329\pi$
$67$			13.2842i			1.62293i	−0.584403	+	0.811464i	$0.698671\pi$
$68$	−0.285764	+	7.17300i	−0.0346540	+	0.869854i
$69$	6.32167	−	13.1271i	0.761040	−	1.58032i
$70$	8.10668	+	6.34997i	0.968933	+	0.758967i
$71$	1.49968	+	3.11413i	0.177980	+	0.369579i	0.970805	−	0.239870i	$-0.0771049\pi$
$71$	1.49968	+	3.11413i	0.177980	+	0.369579i	−0.792825	+	0.609449i	$0.791391\pi$
$72$	1.52896	+	3.72944i	0.180190	+	0.439519i
$73$	−8.97767	−	2.04910i	−1.05076	−	0.239828i	−0.337932	−	0.941170i	$-0.609727\pi$
$73$	−8.97767	−	2.04910i	−1.05076	−	0.239828i	−0.712825	+	0.701342i	$0.752585\pi$
$74$	14.6226	+	3.64524i	1.69984	+	0.423750i
$75$	4.87900	−	2.34960i	0.563378	−	0.271309i
$76$	−3.10009	+	1.34364i	−0.355605	+	0.154127i
$77$	3.42572	+	13.2486i	0.390397	+	1.50981i
$78$	12.0169	+	6.08463i	1.36064	+	0.688949i
$79$		−	4.00244i		−	0.450309i	−0.974323	−	0.225155i	$-0.927711\pi$
$79$		−	4.00244i		−	0.450309i	0.974323	−	0.225155i	$-0.0722887\pi$
$80$	−0.875748	+	10.9737i	−0.0979116	+	1.22690i
$81$	10.1308	+	4.87876i	1.12565	+	0.542084i
$82$	−2.83283	+	3.41069i	−0.312834	+	0.376648i
$83$	0.261589	−	1.14609i	0.0287131	−	0.125800i	−0.958540	−	0.284957i	$-0.908021\pi$
$83$	0.261589	−	1.14609i	0.0287131	−	0.125800i	0.987253	+	0.159157i	$0.0508777\pi$
$84$	4.94149	−	9.97414i	0.539161	−	1.08827i
$85$	−2.19815	−	9.63073i	−0.238423	−	1.04460i
$86$	−1.29835	−	0.657409i	−0.140005	−	0.0708902i
$87$	−1.36518	−	5.98125i	−0.146363	−	0.641257i
$88$	−9.78756	+	10.8727i	−1.04336	+	1.15903i
$89$	12.0984	+	2.76138i	1.28243	+	0.292705i	0.808833	−	0.588039i	$-0.200100\pi$
$89$	12.0984	+	2.76138i	1.28243	+	0.292705i	0.473593	+	0.880744i	$0.342957\pi$
$90$	−3.37119	−	4.40444i	−0.355355	−	0.464268i
$91$	−2.99886	−	11.5977i	−0.314365	−	1.21577i
$92$	−10.4779	−	9.06119i	−1.09240	−	0.944694i
$93$	−2.86557	−	3.59331i	−0.297146	−	0.372609i
$94$	1.54339	+	3.37516i	0.159188	+	0.348121i
$95$	3.63505	−	2.89886i	0.372949	−	0.297417i
$96$	11.8070	−	1.48188i	1.20505	−	0.151243i
$97$			2.97945i			0.302518i	0.988494	+	0.151259i	$0.0483327\pi$
$97$			2.97945i			0.302518i	−0.988494	+	0.151259i	$0.951667\pi$
$98$	−9.56229	+	2.56174i	−0.965938	+	0.258775i
$99$		−	7.37069i		−	0.740782i
$100$	−0.944954	−	5.06116i	−0.0944954	−	0.506116i
$101$	10.8317	−	8.63801i	1.07780	−	0.859514i	0.0871812	−	0.996192i	$-0.472214\pi$
$101$	10.8317	−	8.63801i	1.07780	−	0.859514i	0.990615	+	0.136678i	$0.0436427\pi$
$102$	−9.71087	+	4.44057i	−0.961520	+	0.439682i
$103$	2.03455	+	2.55124i	0.200470	+	0.251381i	0.871897	−	0.489689i	$-0.162890\pi$
$103$	2.03455	+	2.55124i	0.200470	+	0.251381i	−0.671427	+	0.741071i	$0.734318\pi$
$104$	8.56797	−	9.51786i	0.840159	−	0.933303i
$105$	−2.97951	+	15.0247i	−0.290770	+	1.46626i
$106$	4.80097	−	3.67470i	0.466311	−	0.356918i
$107$	6.21411	+	1.41833i	0.600740	+	0.137115i	0.512067	−	0.858946i	$-0.328880\pi$
$107$	6.21411	+	1.41833i	0.600740	+	0.137115i	0.0886736	+	0.996061i	$0.471737\pi$
$108$	4.33420	−	5.01187i	0.417058	−	0.482267i
$109$	−0.236079	−	1.03433i	−0.0226122	−	0.0990706i	0.962363	−	0.271769i	$-0.0876086\pi$
$109$	−0.236079	−	1.03433i	−0.0226122	−	0.0990706i	−0.984975	+	0.172698i	$0.944751\pi$
$110$	9.09374	−	17.9597i	0.867054	−	1.71239i
$111$	4.98806	+	21.8541i	0.473446	+	2.07430i
$112$	−7.92697	−	7.01165i	−0.749028	−	0.662538i
$113$	2.84764	−	12.4763i	0.267883	−	1.17367i	−0.644587	−	0.764531i	$-0.722971\pi$
$113$	2.84764	−	12.4763i	0.267883	−	1.17367i	0.912471	−	0.409142i	$-0.134172\pi$
$114$	−3.86613	−	3.21111i	−0.362096	−	0.300748i
$115$	17.1743	+	8.27073i	1.60152	+	0.771249i
$116$	−5.82835	−	0.232194i	−0.541148	−	0.0215587i
$117$			6.45225i			0.596511i
$118$	−1.55012	+	3.06141i	−0.142700	+	0.281826i
$119$	8.67051	+	3.87375i	0.794825	+	0.355106i
$120$	−15.1510	+	6.21146i	−1.38309	+	0.567026i
$121$	14.1915	−	6.83428i	1.29014	−	0.621298i
$122$	−4.00892	+	16.0815i	−0.362950	+	1.45595i
$123$	−6.42961	−	1.46752i	−0.579738	−	0.132321i
$124$	−4.00931	+	1.73772i	−0.360047	+	0.156052i
$125$	−2.89654	−	6.01473i	−0.259075	−	0.537974i
$126$	5.33190	−	0.0465099i	0.475004	−	0.00414343i
$127$	3.12141	−	6.48167i	0.276980	−	0.575155i	−0.715351	−	0.698766i	$-0.753733\pi$
$127$	3.12141	−	6.48167i	0.276980	−	0.575155i	0.992331	+	0.123610i	$0.0394473\pi$
$128$	1.57160	−	11.2040i	0.138912	−	0.990305i
$129$		−	2.16470i		−	0.190591i
$130$	−7.96060	+	15.7218i	−0.698191	+	1.37889i
$131$	−5.94039	+	7.44901i	−0.519014	+	0.650823i	−0.970399	−	0.241506i	$-0.922359\pi$
$131$	−5.94039	+	7.44901i	−0.519014	+	0.650823i	0.451385	+	0.892329i	$0.350930\pi$
$132$	−21.0051	−	5.68276i	−1.82826	−	0.494621i
$133$	0.127956	+	4.46784i	0.0110952	+	0.387410i
$134$	3.81499	+	18.3953i	0.329565	+	1.58911i
$135$	−3.95610	+	8.21493i	−0.340487	+	0.707029i
$136$	1.66425	+	10.0149i	0.142708	+	0.858767i
$137$	−4.85034	+	6.08213i	−0.414392	+	0.519631i	−0.944594	−	0.328240i	$-0.893545\pi$
$137$	−4.85034	+	6.08213i	−0.414392	+	0.519631i	0.530202	+	0.847871i	$0.322116\pi$
$138$	4.98406	−	19.9932i	0.424271	−	1.70193i
$139$	−4.55940	−	5.71730i	−0.386723	−	0.484935i	0.549922	−	0.835216i	$-0.314658\pi$
$139$	−4.55940	−	5.71730i	−0.386723	−	0.484935i	−0.936645	+	0.350281i	$0.886086\pi$
$140$	13.0493	+	6.46502i	1.10287	+	0.546394i
$141$	−3.44191	+	4.31602i	−0.289861	+	0.363475i
$142$	2.97101	+	3.88160i	0.249321	+	0.325736i
$143$	−21.0989	+	10.1607i	−1.76438	+	0.849680i
$144$	3.18826	+	4.72525i	0.265688	+	0.393771i
$145$	7.82535	−	1.78609i	0.649860	−	0.148326i
$146$	−13.0203	−	0.259253i	−1.07757	−	0.0214560i
$147$	−9.82478	−	10.9682i	−0.810334	−	0.904644i
$148$	21.2955	+	0.848386i	1.75048	+	0.0697369i
$149$	1.46650	+	6.42516i	0.120140	+	0.526369i	0.998802	+	0.0489252i	$0.0155796\pi$
$149$	1.46650	+	6.42516i	0.120140	+	0.526369i	−0.878662	+	0.477444i	$0.841563\pi$
$150$	6.08142	−	4.65477i	0.496546	−	0.380060i
$151$	−8.80109	−	18.2757i	−0.716223	−	1.48725i	−0.866801	−	0.498654i	$-0.833828\pi$
$151$	−8.80109	−	18.2757i	−0.716223	−	1.48725i	0.150579	−	0.988598i	$-0.451886\pi$
$152$	−3.90698	+	2.75090i	−0.316898	+	0.223127i
$153$	−3.99911	−	3.18918i	−0.323309	−	0.257830i
$154$	8.54851	+	17.3621i	0.688859	+	1.39908i
$155$	4.70117	−	3.74906i	0.377607	−	0.301132i
$156$	18.3877	+	4.97465i	1.47220	+	0.398291i
$157$	−14.6082	−	11.6496i	−1.16586	−	0.929741i	−0.167435	−	0.985883i	$-0.553549\pi$
$157$	−14.6082	−	11.6496i	−1.16586	−	0.929741i	−0.998423	+	0.0561423i	$0.982120\pi$
$158$	−1.14943	−	5.54236i	−0.0914436	−	0.440927i
$159$	8.10241	+	3.90192i	0.642563	+	0.309442i
$160$	1.93876	+	15.4473i	0.153272	+	1.22122i
$161$	−16.2760	+	8.42039i	−1.28273	+	0.663619i
$162$	15.4298	+	3.84645i	1.21228	+	0.302206i
$163$	13.4632	+	10.7365i	1.05452	+	0.840949i	0.987629	−	0.156811i	$-0.0501214\pi$
$163$	13.4632	+	10.7365i	1.05452	+	0.840949i	0.0668885	+	0.997760i	$0.478693\pi$
$164$	−2.94327	+	5.53649i	−0.229831	+	0.432327i
$165$	29.9437			2.33111
$166$	0.0330964	−	1.66218i	0.00256878	−	0.129010i
$167$	−0.0376482	−	0.0181304i	−0.00291331	−	0.00140297i	0.432427	−	0.901669i	$-0.357657\pi$
$167$	−0.0376482	−	0.0181304i	−0.00291331	−	0.00140297i	−0.435340	+	0.900266i	$0.643372\pi$
$168$	3.97832	−	15.2308i	0.306934	−	1.17508i
$169$	6.75725	−	3.25412i	0.519789	−	0.250317i
$170$	−5.80966	−	12.7049i	−0.445581	−	0.974419i
$171$	0.535712	−	2.34711i	0.0409670	−	0.179488i
$172$	−1.98668	−	0.537482i	−0.151483	−	0.0409826i
$173$	−5.73277	−	11.9042i	−0.435854	−	0.905060i	−0.997004	−	0.0773463i	$-0.975355\pi$
$173$	−5.73277	−	11.9042i	−0.435854	−	0.905060i	0.561150	−	0.827714i	$-0.310359\pi$
$174$	−3.60814	−	7.89047i	−0.273532	−	0.598175i
$175$	−6.68089	−	1.32487i	−0.505028	−	0.100151i
$176$	−10.4309	+	17.8667i	−0.786257	+	1.34675i
$177$	−5.10420			−0.383655
$178$	17.5462	+	0.349372i	1.31514	+	0.0261865i
$179$	4.54679	−	9.44150i	0.339843	−	0.705691i	−0.659081	−	0.752072i	$-0.729055\pi$
$179$	4.54679	−	9.44150i	0.339843	−	0.705691i	0.998924	+	0.0463810i	$0.0147688\pi$
$180$	−5.93312	−	5.13089i	−0.442229	−	0.382434i
$181$	6.52436	+	1.48914i	0.484952	+	0.110687i	0.458005	−	0.888950i	$-0.348564\pi$
$181$	6.52436	+	1.48914i	0.484952	+	0.110687i	0.0269471	+	0.999637i	$0.491421\pi$
$182$	−7.48331	−	15.1987i	−0.554700	−	1.12660i
$183$	−24.0345	+	5.48571i	−1.77668	+	0.405516i
$184$	−17.1115	−	9.53838i	−1.26148	−	0.703179i
$185$	−28.5921	+	6.52595i	−2.10213	+	0.479797i
$186$	−5.00002	−	4.15289i	−0.366619	−	0.304504i
$187$	4.13104	−	18.0993i	0.302092	−	1.32355i
$188$	3.10648	+	4.23051i	0.226564	+	0.308541i
$189$	−4.02769	−	7.78524i	−0.292971	−	0.566293i
$190$	4.20113	−	5.05811i	0.304782	−	0.366954i
$191$	−0.761958	+	0.607641i	−0.0551334	+	0.0439674i	−0.650669	−	0.759362i	$-0.725511\pi$
$191$	−0.761958	+	0.607641i	−0.0551334	+	0.0439674i	0.595535	+	0.803329i	$0.296940\pi$
$192$	15.9242	−	5.44279i	1.14923	−	0.392800i
$193$	−6.31736	−	7.92172i	−0.454733	−	0.570218i	0.500626	−	0.865664i	$-0.333103\pi$
$193$	−6.31736	−	7.92172i	−0.454733	−	0.570218i	−0.955359	+	0.295446i	$0.904532\pi$
$194$	0.855645	+	4.12579i	0.0614318	+	0.296214i
$195$	−26.2125			−1.87711
$196$	−12.5057	+	6.29349i	−0.893263	+	0.449535i
$197$	−13.6250			−0.970743			−0.485372	−	0.874308i	$-0.661316\pi$
$197$	−13.6250			−0.970743			−0.485372	+	0.874308i	$0.661316\pi$
$198$	−2.11673	−	10.2065i	−0.150429	−	0.725347i
$199$	−8.18702	−	10.2662i	−0.580362	−	0.727752i	0.401812	−	0.915722i	$-0.368380\pi$
$199$	−8.18702	−	10.2662i	−0.580362	−	0.727752i	−0.982175	+	0.187971i	$0.939809\pi$
$200$	−2.76200	−	6.73706i	−0.195303	−	0.476382i
$201$	−21.8479	+	17.4231i	−1.54103	+	1.22893i
$202$	12.5185	−	15.0721i	0.880800	−	1.06047i
$203$	−3.14758	+	7.04514i	−0.220917	+	0.494472i
$204$	−12.1719	+	8.93786i	−0.852200	+	0.625775i
$205$	1.91997	−	8.41194i	0.134097	−	0.587516i
$206$	3.55001	+	2.94854i	0.247341	+	0.205435i
$207$	9.62290	−	2.19636i	0.668838	−	0.152658i
$208$	9.13112	−	15.6404i	0.633129	−	1.08447i
$209$	8.51867	−	1.94433i	0.589249	−	0.134492i
$210$	0.188948	+	21.6610i	0.0130387	+	1.49475i
$211$	25.6087	+	5.84501i	1.76297	+	0.402387i	0.976549	−	0.215297i	$-0.0690721\pi$
$211$	25.6087	+	5.84501i	1.76297	+	0.402387i	0.786426	+	0.617685i	$0.211929\pi$
$212$	5.59282	−	6.46728i	0.384116	−	0.444175i
$213$	−3.15471	+	6.55082i	−0.216157	+	0.448855i
$214$	9.01229	+	0.179448i	0.616067	+	0.0122668i
$215$	2.83211			0.193148
$216$	4.56245	−	8.18488i	0.310436	−	0.556910i
$217$	0.165484	+	5.77820i	0.0112338	+	0.392250i
$218$	−0.623950	−	1.36449i	−0.0422592	−	0.0924146i
$219$	−8.40474	−	17.4526i	−0.567940	−	1.17934i
$220$	7.43483	−	27.4812i	0.501256	−	1.85278i
$221$	−3.61629	+	15.8440i	−0.243258	+	1.06578i
$222$	13.1833	+	28.8300i	0.884807	+	1.93494i
$223$	−8.82199	+	4.24845i	−0.590764	+	0.284497i	−0.705285	−	0.708924i	$-0.749181\pi$
$223$	−8.82199	+	4.24845i	−0.590764	+	0.284497i	0.114521	+	0.993421i	$0.463467\pi$
$224$	−12.9905	−	7.43288i	−0.867962	−	0.496630i
$225$	3.30526	+	1.59173i	0.220351	+	0.106115i
$226$	0.360286	−	18.0943i	0.0239658	−	1.20362i
$227$	−16.6986			−1.10833			−0.554163	−	0.832408i	$-0.686962\pi$
$227$	−16.6986			−1.10833			−0.554163	+	0.832408i	$0.686962\pi$
$228$	−6.27579	−	3.33629i	−0.415624	−	0.220951i
$229$	−16.2562	−	12.9639i	−1.07424	−	0.856677i	−0.0840565	−	0.996461i	$-0.526788\pi$
$229$	−16.2562	−	12.9639i	−1.07424	−	0.856677i	−0.990182	+	0.139784i	$0.955359\pi$
$230$	26.1573	+	6.52071i	1.72476	+	0.429963i
$231$	−17.2962	+	23.0104i	−1.13800	+	1.51397i
$232$	−8.13747	+	1.35227i	−0.534251	+	0.0887806i
$233$	12.4902	+	6.01495i	0.818259	+	0.394053i	0.795699	−	0.605693i	$-0.207104\pi$
$233$	12.4902	+	6.01495i	0.818259	+	0.394053i	0.0225603	+	0.999745i	$0.492818\pi$
$234$	1.85297	+	8.93474i	0.121133	+	0.584082i
$235$	−5.64671	−	4.50310i	−0.368351	−	0.293750i
$236$	−1.26734	+	4.68445i	−0.0824969	+	0.304932i
$237$	6.58260	−	5.24945i	0.427586	−	0.340988i
$238$	13.1189	+	2.87416i	0.850375	+	0.186304i
$239$	7.78316	+	6.20687i	0.503451	+	0.401489i	0.842015	−	0.539455i	$-0.181370\pi$
$239$	7.78316	+	6.20687i	0.503451	+	0.401489i	−0.338564	+	0.940944i	$0.609941\pi$
$240$	−19.1965	+	12.9524i	−1.23913	+	0.836074i
$241$	2.53901	+	5.27230i	0.163552	+	0.339619i	0.966598	−	0.256298i	$-0.0825030\pi$
$241$	2.53901	+	5.27230i	0.163552	+	0.339619i	−0.803046	+	0.595917i	$0.796789\pi$
$242$	17.6890	−	13.5393i	1.13709	−	0.870340i
$243$	3.05176	+	13.3706i	0.195770	+	0.857726i
$244$	−0.933028	+	23.4201i	−0.0597310	+	1.49932i
$245$	14.3499	−	12.8539i	0.916780	−	0.821205i
$246$	−9.32483	−	0.185672i	−0.594530	−	0.0118380i
$247$	−7.45719	+	1.70206i	−0.474490	+	0.108299i
$248$	−5.05285	+	3.55771i	−0.320856	+	0.225915i
$249$	2.22801	−	1.07295i	0.141195	−	0.0679957i
$250$	−5.73831	−	7.49705i	−0.362922	−	0.474155i
$251$	−5.55141	+	6.96125i	−0.350402	+	0.439390i	−0.925531	−	0.378673i	$-0.876381\pi$
$251$	−5.55141	+	6.96125i	−0.350402	+	0.439390i	0.575129	+	0.818063i	$0.304952\pi$
$252$	7.36998	−	1.59563i	0.464265	−	0.100515i
$253$	22.3358	+	28.0082i	1.40424	+	1.76086i
$254$	2.46094	−	9.87189i	0.154413	−	0.619417i
$255$	12.9561	−	16.2465i	0.811346	−	1.01740i
$256$	−1.04132	−	15.9661i	−0.0650824	−	0.997880i
$257$	1.47642	−	3.06581i	0.0920963	−	0.191240i	−0.849832	−	0.527053i	$-0.823297\pi$
$257$	1.47642	−	3.06581i	0.0920963	−	0.191240i	0.941929	+	0.335813i	$0.109011\pi$
$258$	−0.621663	−	2.99756i	−0.0387031	−	0.186620i
$259$	11.5005	−	25.7413i	0.714609	−	1.59949i
$260$	−6.50841	+	24.0569i	−0.403634	+	1.49194i
$261$	2.59134	−	3.24943i	0.160400	−	0.201135i
$262$	−6.08671	+	12.0210i	−0.376038	+	0.742658i
$263$		−	8.97986i		−	0.553722i	−0.960910	−	0.276861i	$-0.910706\pi$
$263$		−	8.97986i		−	0.553722i	0.960910	−	0.276861i	$-0.0892942\pi$
$264$	−30.7187	−	1.83691i	−1.89061	−	0.113054i
$265$	−5.10493	+	10.6005i	−0.313593	+	0.651183i
$266$	1.46027	+	6.15008i	0.0895349	+	0.377085i
$267$	11.3263	+	23.5193i	0.693158	+	1.43936i
$268$	10.5656	+	24.3773i	0.645397	+	1.48908i
$269$	30.7940	+	7.02853i	1.87754	+	0.428537i	0.998810	−	0.0487737i	$-0.0155313\pi$
$269$	30.7940	+	7.02853i	1.87754	+	0.428537i	0.878734	+	0.477311i	$0.158388\pi$
$270$	−3.11902	+	12.5117i	−0.189818	+	0.761439i
$271$	−6.49165	+	3.12622i	−0.394340	+	0.189904i	−0.620536	−	0.784178i	$-0.713085\pi$
$271$	−6.49165	+	3.12622i	−0.394340	+	0.189904i	0.226197	+	0.974082i	$0.427371\pi$
$272$	5.18065	+	13.3901i	0.314123	+	0.811895i
$273$	15.1410	−	20.1432i	0.916372	−	1.21912i
$274$	−4.96981	+	9.81514i	−0.300237	+	0.592955i
$275$			13.3148i			0.802912i
$276$	1.15998	−	29.1168i	0.0698226	−	1.75263i
$277$	1.15076	+	0.554178i	0.0691426	+	0.0332973i	0.468136	−	0.883657i	$-0.344926\pi$
$277$	1.15076	+	0.554178i	0.0691426	+	0.0332973i	−0.398993	+	0.916954i	$0.630640\pi$
$278$	−7.95552	−	6.60765i	−0.477140	−	0.396300i
$279$	0.692830	−	3.03549i	0.0414787	−	0.181730i
$280$	19.9266	+	5.20489i	1.19084	+	0.311052i
$281$	−6.34115	−	27.7824i	−0.378281	−	1.65736i	−0.702731	−	0.711456i	$-0.748036\pi$
$281$	−6.34115	−	27.7824i	−0.378281	−	1.65736i	0.324450	−	0.945903i	$-0.394821\pi$
$282$	−3.52670	+	6.96506i	−0.210012	+	0.414763i
$283$	−1.84538	−	8.08514i	−0.109696	−	0.480611i	−0.999696	−	0.0246503i	$-0.992153\pi$
$283$	−1.84538	−	8.08514i	−0.109696	−	0.480611i	0.890000	−	0.455961i	$-0.150704\pi$
$284$	5.22882	+	4.52181i	0.310273	+	0.268320i
$285$	9.53521	+	2.17635i	0.564817	+	0.128916i
$286$	−26.2987	+	20.1292i	−1.55507	+	1.19027i
$287$	5.35520	+	6.33436i	0.316108	+	0.373905i
$288$	5.77194	+	5.62767i	0.340115	+	0.331613i
$289$	2.56666	+	3.21849i	0.150980	+	0.189323i
$290$	10.3232	−	4.72058i	0.606200	−	0.277202i
$291$	−4.90015	+	3.90774i	−0.287252	+	0.229076i
$292$	−18.1043	+	3.38019i	−1.05947	+	0.197811i
$293$		−	21.7010i		−	1.26779i	−0.773420	−	0.633894i	$-0.781456\pi$
$293$		−	21.7010i		−	1.26779i	0.773420	−	0.633894i	$-0.218544\pi$
$294$	−16.7547	−	12.3667i	−0.977155	−	0.721242i
$295$		−	6.67789i		−	0.388802i
$296$	29.7325	−	4.94087i	1.72816	−	0.287182i
$297$	−13.3970	+	10.6838i	−0.777375	+	0.619936i
$298$	3.87592	+	8.47607i	0.224526	+	0.491006i
$299$	−19.5526	−	24.5182i	−1.13076	−	1.41792i
$300$	7.08447	−	8.19215i	0.409022	−	0.472974i
$301$	−1.63589	+	2.17635i	−0.0942912	+	0.125443i
$302$	−17.4357	−	22.7797i	−1.00331	−	1.31082i
$303$	28.4130	+	6.48508i	1.63228	+	0.372558i
$304$	−4.62017	+	4.93132i	−0.264985	+	0.282830i
$305$	−7.17703	−	31.4446i	−0.410956	−	1.80051i
$306$	−6.45363	−	3.26774i	−0.368929	−	0.186804i
$307$	2.54507	+	11.1507i	0.145255	+	0.636402i	0.994165	+	0.107866i	$0.0344017\pi$
$307$	2.54507	+	11.1507i	0.145255	+	0.636402i	−0.848911	+	0.528536i	$0.822741\pi$
$308$	16.8236	+	21.5872i	0.958614	+	1.23004i
$309$	−1.52746	+	6.69223i	−0.0868940	+	0.380708i
$310$	5.43328	−	6.54160i	0.308589	−	0.371538i
$311$	21.7728	+	10.4852i	1.23462	+	0.594563i	0.933347	−	0.358975i	$-0.116874\pi$
$311$	21.7728	+	10.4852i	1.23462	+	0.594563i	0.301275	+	0.953537i	$0.402588\pi$
$312$	26.8910	+	1.60802i	1.52240	+	0.0910362i
$313$		−	0.769036i		−	0.0434685i	−0.999764	−	0.0217342i	$-0.993081\pi$
$313$		−	0.769036i		−	0.0434685i	0.999764	−	0.0217342i	$-0.00691877\pi$
$314$	−23.5742	−	11.9366i	−1.33037	−	0.673620i
$315$	−9.21628	+	4.76803i	−0.519278	+	0.268648i
$316$	−3.18333	−	7.34468i	−0.179077	−	0.413171i
$317$	−12.7385	+	6.13452i	−0.715463	+	0.344549i	−0.755948	−	0.654631i	$-0.772824\pi$
$317$	−12.7385	+	6.13452i	−0.715463	+	0.344549i	0.0404855	+	0.999180i	$0.487110\pi$
$318$	12.3404	+	3.07630i	0.692013	+	0.172510i
$319$	14.7064	+	3.35663i	0.823399	+	0.187935i
$320$	7.12088	+	20.8338i	0.398069	+	1.16465i
$321$	5.81754	+	12.0802i	0.324703	+	0.674254i
$322$	−20.1200	+	16.3343i	−1.12124	+	0.910275i
$323$	2.63096	−	5.46325i	0.146391	−	0.303983i
$324$	22.4709	+	0.895216i	1.24839	+	0.0497342i
$325$		−	11.6557i		−	0.646541i
$326$	21.7264	+	11.0010i	1.20332	+	0.609289i
$327$	1.39147	−	1.74485i	0.0769486	−	0.0964905i
$328$	−2.48570	+	8.51190i	−0.137250	+	0.469991i
$329$	6.72211	−	1.73816i	0.370602	−	0.0958278i
$330$	41.4644	−	8.59928i	2.28254	−	0.473375i
$331$	1.29330	−	2.68555i	0.0710859	−	0.147611i	−0.862398	−	0.506231i	$-0.831038\pi$
$331$	1.29330	−	2.68555i	0.0710859	−	0.147611i	0.933484	+	0.358620i	$0.116753\pi$
$332$	−0.431517	−	2.31120i	−0.0236826	−	0.126843i
$333$	−9.46815	+	11.8727i	−0.518852	+	0.650619i
$334$	−0.0573400	−	0.0142942i	−0.00313751	−	0.000782142i
$335$	−22.7949	−	28.5839i	−1.24542	−	1.56170i
$336$	1.13497	−	22.2333i	0.0619176	−	1.21293i
$337$	−7.69347	+	9.64731i	−0.419090	+	0.525522i	−0.945899	−	0.324461i	$-0.894817\pi$
$337$	−7.69347	+	9.64731i	−0.419090	+	0.525522i	0.526809	+	0.849984i	$0.323388\pi$
$338$	8.42256	−	6.44670i	0.458127	−	0.350654i
$339$	24.2540	−	11.6801i	1.31730	−	0.634377i
$340$	−11.6935	−	15.9246i	−0.634170	−	0.863633i
$341$	11.0171	−	2.51458i	0.596609	−	0.136172i
$342$	0.0677788	−	3.40400i	0.00366506	−	0.184067i
$343$	1.58884	+	18.4520i	0.0857893	+	0.996313i
$344$	−2.90541	−	0.173737i	−0.156649	−	0.00936728i
$345$	8.92280	+	39.0933i	0.480387	+	2.10471i
$346$	−11.3571	−	14.8380i	−0.610562	−	0.797695i
$347$	3.83747	+	7.96860i	0.206006	+	0.427777i	0.978216	−	0.207592i	$-0.0665625\pi$
$347$	3.83747	+	7.96860i	0.206006	+	0.427777i	−0.772209	+	0.635368i	$0.780848\pi$
$348$	−7.26237	−	9.89012i	−0.389304	−	0.530166i
$349$	10.4432	+	8.32819i	0.559013	+	0.445798i	0.861791	−	0.507263i	$-0.169343\pi$
$349$	10.4432	+	8.32819i	0.559013	+	0.445798i	−0.302779	+	0.953061i	$0.597914\pi$
$350$	−9.63182	+	0.0840180i	−0.514843	+	0.00449095i
$351$	11.7277	−	9.35252i	0.625978	−	0.499201i
$352$	−9.31313	+	27.7365i	−0.496391	+	1.47836i
$353$	13.5359	+	10.7946i	0.720446	+	0.574536i	0.913591	−	0.406634i	$-0.133298\pi$
$353$	13.5359	+	10.7946i	0.720446	+	0.574536i	−0.193145	+	0.981170i	$0.561869\pi$
$354$	−7.06802	+	1.46583i	−0.375661	+	0.0779082i
$355$	−8.57053	−	4.12735i	−0.454877	−	0.219057i
$356$	24.3974	−	4.55517i	1.29306	−	0.241423i
$357$	5.00096	+	19.3406i	0.264679	+	1.02361i
$358$	3.58472	−	14.3799i	0.189459	−	0.759999i
$359$	16.7079	+	13.3241i	0.881808	+	0.703218i	0.955793	−	0.294041i	$-0.0950002\pi$
$359$	16.7079	+	13.3241i	0.881808	+	0.703218i	−0.0739849	+	0.997259i	$0.523572\pi$
$360$	−9.68938	−	5.40110i	−0.510675	−	0.284663i
$361$	−16.1460			−0.849790
$362$	9.46225	+	0.188408i	0.497325	+	0.00990249i
$363$	29.8531	+	14.3765i	1.56688	+	0.754570i
$364$	−14.7273	−	18.8973i	−0.771920	−	0.990486i
$365$	22.8335	−	10.9960i	1.19516	−	0.575559i
$366$	−31.7063	+	14.4986i	−1.65731	+	0.757854i
$367$	−2.30913	+	10.1170i	−0.120536	+	0.528102i	0.878221	+	0.478255i	$0.158730\pi$
$367$	−2.30913	+	10.1170i	−0.120536	+	0.528102i	−0.998757	+	0.0498468i	$0.984127\pi$
$368$	−26.4344	−	8.29413i	−1.37799	−	0.432361i
$369$	−1.93848	−	4.02529i	−0.100913	−	0.209548i
$370$	−37.7186	+	17.2479i	−1.96090	+	0.896677i
$371$	−5.19730	−	10.0460i	−0.269830	−	0.521563i
$372$	−8.11640	−	4.31478i	−0.420816	−	0.223711i
$373$	−9.57610			−0.495831			−0.247916	−	0.968782i	$-0.579746\pi$
$373$	−9.57610			−0.495831			−0.247916	+	0.968782i	$0.579746\pi$
$374$	0.522663	−	26.2493i	0.0270263	−	1.35732i
$375$	6.09312	−	12.6525i	0.314647	−	0.653372i
$376$	5.51662	+	4.96606i	0.284498	+	0.256105i
$377$	−12.8739	−	2.93838i	−0.663038	−	0.151334i
$378$	−7.81311	−	9.62391i	−0.401863	−	0.495000i
$379$	−8.72335	+	1.99105i	−0.448088	+	0.102273i	−0.440610	−	0.897699i	$-0.645238\pi$
$379$	−8.72335	+	1.99105i	−0.448088	+	0.102273i	−0.00747858	+	0.999972i	$0.502381\pi$
$380$	4.36491	−	8.21070i	0.223915	−	0.421200i
$381$	14.7540	−	3.36750i	0.755870	−	0.172522i
$382$	−0.880616	+	1.06025i	−0.0450562	+	0.0542472i
$383$	−6.02445	+	26.3949i	−0.307835	+	1.34871i	0.550161	+	0.835058i	$0.314566\pi$
$383$	−6.02445	+	26.3949i	−0.307835	+	1.34871i	−0.857996	+	0.513656i	$0.828291\pi$
$384$	20.4879	−	12.1100i	1.04552	−	0.617988i
$385$	−30.1048	−	22.6288i	−1.53429	−	1.15327i
$386$	−11.0229	−	9.15535i	−0.561052	−	0.465995i
$387$	1.14653	−	0.914328i	0.0582814	−	0.0464779i
$388$	2.36971	+	5.46745i	0.120304	+	0.277568i
$389$	−3.37734	−	4.23505i	−0.171238	−	0.214725i	0.688806	−	0.724946i	$-0.258135\pi$
$389$	−3.37734	−	4.23505i	−0.171238	−	0.214725i	−0.860044	+	0.510220i	$0.829564\pi$
$390$	−36.2977	+	7.52776i	−1.83800	+	0.381183i
$391$	24.8607			1.25726
$392$	−15.5098	+	12.3063i	−0.783365	+	0.621562i
$393$	−20.0422			−1.01099
$394$	−18.8672	+	3.91287i	−0.950518	+	0.197127i
$395$	6.86792	+	8.61210i	0.345563	+	0.433322i
$396$	−5.86227	−	13.5256i	−0.294590	−	0.679687i
$397$	−29.1515	+	23.2476i	−1.46307	+	1.16676i	−0.511524	+	0.859269i	$0.670919\pi$
$397$	−29.1515	+	23.2476i	−1.46307	+	1.16676i	−0.951550	+	0.307493i	$0.900510\pi$
$398$	−14.2852	−	11.8649i	−0.716054	−	0.594735i
$399$	−7.18019	+	6.07029i	−0.359459	+	0.303895i
$400$	−5.75943	−	8.53593i	−0.287972	−	0.426797i
$401$	2.83819	−	12.4349i	0.141732	−	0.620970i	−0.853300	−	0.521420i	$-0.825403\pi$
$401$	2.83819	−	12.4349i	0.141732	−	0.620970i	0.995033	−	0.0995498i	$-0.0317403\pi$
$402$	−25.2502	+	30.4009i	−1.25937	+	1.51626i
$403$	−9.64430	+	2.20125i	−0.480417	+	0.109652i
$404$	13.0065	−	24.4662i	0.647100	−	1.21724i
$405$	−30.1703	+	6.88618i	−1.49917	+	0.342177i
$406$	−2.33537	+	10.6597i	−0.115902	+	0.529030i
$407$	−53.7337	−	12.2644i	−2.66348	−	0.607923i
$408$	−14.2882	+	15.8722i	−0.707369	+	0.785792i
$409$	7.67598	−	15.9393i	0.379553	−	0.788150i	−0.620439	−	0.784254i	$-0.713046\pi$
$409$	7.67598	−	15.9393i	0.379553	−	0.788150i	0.999992	−	0.00389554i	$-0.00123999\pi$
$410$	0.242917	−	12.1998i	0.0119968	−	0.602505i
$411$	−16.3645			−0.807200
$412$	5.76263	+	3.06349i	0.283904	+	0.150927i
$413$	5.13167	+	3.85731i	0.252513	+	0.189806i
$414$	12.6945	−	5.80494i	0.623902	−	0.285297i
$415$	1.40376	+	2.91494i	0.0689079	+	0.143089i
$416$	8.15265	−	24.2803i	0.399717	−	1.19044i
$417$	3.42301	−	14.9972i	0.167626	−	0.734416i
$418$	11.2378	−	5.13882i	0.549661	−	0.251348i
$419$	8.56384	−	4.12413i	0.418371	−	0.201477i	−0.212842	−	0.977087i	$-0.568272\pi$
$419$	8.56384	−	4.12413i	0.418371	−	0.201477i	0.631213	+	0.775610i	$0.282558\pi$
$420$	6.48230	+	29.9408i	0.316304	+	1.46096i
$421$	−17.7403	−	8.54328i	−0.864609	−	0.416374i	−0.0516297	−	0.998666i	$-0.516442\pi$
$421$	−17.7403	−	8.54328i	−0.864609	−	0.416374i	−0.812979	+	0.582293i	$0.802156\pi$
$422$	37.1401	+	0.739517i	1.80795	+	0.0359991i
$423$	−3.73977			−0.181834
$424$	5.88736	−	10.5617i	0.285915	−	0.512922i
$425$	7.22419	+	5.76110i	0.350425	+	0.279455i
$426$	−2.48720	+	9.97722i	−0.120505	+	0.483398i
$427$	28.3095	+	12.6479i	1.36999	+	0.612076i
$428$	12.5313	−	2.33968i	0.605722	−	0.113093i
$429$	−44.3833	−	21.3739i	−2.14285	−	1.03194i
$430$	3.92175	−	0.813330i	0.189124	−	0.0392223i
$431$	−8.34212	−	6.65262i	−0.401826	−	0.320445i	0.401639	−	0.915798i	$-0.368441\pi$
$431$	−8.34212	−	6.65262i	−0.401826	−	0.320445i	−0.803464	+	0.595353i	$0.797012\pi$
$432$	3.96729	−	12.6442i	0.190877	−	0.608346i
$433$	14.3008	−	11.4045i	0.687254	−	0.548067i	−0.216413	−	0.976302i	$-0.569436\pi$
$433$	14.3008	−	11.4045i	0.687254	−	0.548067i	0.903667	+	0.428235i	$0.140864\pi$
$434$	1.88855	+	7.95382i	0.0906533	+	0.381796i
$435$	13.2009	+	10.5274i	0.632936	+	0.504749i
$436$	−1.25587	−	1.71028i	−0.0601452	−	0.0819076i
$437$	5.07690	+	10.5423i	0.242861	+	0.504306i
$438$	−16.6505	−	21.7538i	−0.795593	−	1.03944i
$439$	−6.76654	−	29.6462i	−0.322949	−	1.41493i	−0.832276	−	0.554361i	$-0.812963\pi$
$439$	−6.76654	−	29.6462i	−0.322949	−	1.41493i	0.509327	−	0.860573i	$-0.329894\pi$
$440$	2.40325	−	40.1897i	0.114571	−	1.91597i
$441$	1.65951	−	9.83645i	0.0790242	−	0.468402i
$442$	−0.457536	+	22.9785i	−0.0217628	+	1.09297i
$443$	18.1146	−	4.13455i	0.860653	−	0.196438i	0.230655	−	0.973036i	$-0.425913\pi$
$443$	18.1146	−	4.13455i	0.860653	−	0.196438i	0.629998	+	0.776597i	$0.283056\pi$
$444$	26.5350	+	36.1362i	1.25930	+	1.71495i
$445$	−30.7706	+	14.8183i	−1.45867	+	0.702457i
$446$	−10.9962	+	8.41654i	−0.520683	+	0.398535i
$447$	−8.64372	+	10.8389i	−0.408834	+	0.512661i
$448$	−20.1231	−	6.56203i	−0.950728	−	0.310027i
$449$	0.385716	+	0.483673i	0.0182031	+	0.0228259i	0.790850	−	0.612010i	$-0.209639\pi$
$449$	0.385716	+	0.483673i	0.0182031	+	0.0228259i	−0.772647	+	0.634836i	$0.781068\pi$
$450$	5.03407	+	1.25493i	0.237308	+	0.0591581i
$451$	10.1101	−	12.6777i	0.476065	−	0.596967i
$452$	−4.69746	−	25.1596i	−0.220950	−	1.18341i
$453$	18.5138	−	38.4444i	0.869856	−	1.80627i
$454$	−23.1234	+	4.79554i	−1.08523	+	0.225066i
$455$	26.3536	+	19.8091i	1.23548	+	0.928666i
$456$	−9.64851	−	2.81762i	−0.451833	−	0.131947i
$457$	15.5436	−	19.4911i	0.727100	−	0.911754i	−0.271617	−	0.962406i	$-0.587558\pi$
$457$	15.5436	−	19.4911i	0.727100	−	0.911754i	0.998716	+	0.0506512i	$0.0161297\pi$
$458$	−26.2337	−	13.2832i	−1.22582	−	0.620683i
$459$			11.8915i			0.555049i
$460$	38.0940	+	1.51762i	1.77614	+	0.0707593i
$461$	−16.1258	+	33.4856i	−0.751055	+	1.55958i	0.0757727	+	0.997125i	$0.475858\pi$
$461$	−16.1258	+	33.4856i	−0.751055	+	1.55958i	−0.826827	+	0.562456i	$0.809857\pi$
$462$	−17.3426	+	36.8308i	−0.806853	+	1.71352i
$463$	10.2266	+	21.2357i	0.475268	+	0.986905i	0.991457	+	0.130430i	$0.0416358\pi$
$463$	10.2266	+	21.2357i	0.475268	+	0.986905i	−0.516189	+	0.856475i	$0.672650\pi$
$464$	−10.8800	+	4.20948i	−0.505091	+	0.195420i
$465$	12.3318	+	2.81465i	0.571872	+	0.130526i
$466$	19.0231	+	4.74224i	0.881230	+	0.219680i
$467$	21.7051	−	10.4526i	1.00439	−	0.483690i	0.141966	−	0.989872i	$-0.454658\pi$
$467$	21.7051	−	10.4526i	1.00439	−	0.483690i	0.862427	+	0.506181i	$0.168943\pi$
$468$	5.13180	+	11.8402i	0.237217	+	0.547315i
$469$	35.1324	−	1.00617i	1.62226	−	0.0464607i
$470$	−9.11248	−	4.61402i	−0.420327	−	0.212829i
$471$		−	39.3045i		−	1.81106i
$472$	−0.409659	+	6.85074i	−0.0188561	+	0.315331i
$473$	4.79536	+	2.30932i	0.220491	+	0.106183i
$474$	7.60769	−	9.15956i	0.349433	−	0.420713i
$475$	−0.967739	+	4.23994i	−0.0444029	+	0.194542i
$476$	18.9918	+	0.212454i	0.870490	+	0.00973783i
$477$	1.35566	+	5.93953i	0.0620713	+	0.271952i
$478$	12.5602	+	6.35976i	0.574491	+	0.290889i
$479$	−2.11086	−	9.24830i	−0.0964478	−	0.422565i	0.903535	−	0.428515i	$-0.140963\pi$
$479$	−2.11086	−	9.24830i	−0.0964478	−	0.422565i	−0.999982	+	0.00594995i	$0.998106\pi$
$480$	−22.8626	+	23.4487i	−1.04353	+	1.07028i
$481$	47.0382	+	10.7362i	2.14476	+	0.489527i
$482$	5.02999	+	6.57165i	0.229110	+	0.299330i
$483$	−35.1956	−	15.7245i	−1.60146	−	0.715487i
$484$	20.6066	−	23.8285i	0.936662	−	1.08311i
$485$	−5.11255	−	6.41093i	−0.232149	−	0.291105i
$486$	8.06572	+	17.6385i	0.365869	+	0.800101i
$487$	−13.0469	+	10.4046i	−0.591213	+	0.471477i	−0.872813	−	0.488055i	$-0.837706\pi$
$487$	−13.0469	+	10.4046i	−0.591213	+	0.471477i	0.281600	+	0.959532i	$0.409135\pi$
$488$	5.43381	+	32.6988i	0.245977	+	1.48021i
$489$			36.2238i			1.63810i
$490$	16.1795	−	21.9204i	0.730917	−	0.990264i
$491$			20.5029i			0.925282i	0.886546	+	0.462641i	$0.153098\pi$
$491$			20.5029i			0.925282i	−0.886546	+	0.462641i	$0.846902\pi$
$492$	−12.9659	+	2.42082i	−0.584546	+	0.109139i
$493$	8.18442	−	6.52686i	0.368608	−	0.293955i
$494$	−9.83753	+	4.49849i	−0.442612	+	0.202397i
$495$	12.6476	+	15.8596i	0.568468	+	0.712837i
$496$	−5.97521	+	6.37761i	−0.268295	+	0.286363i
$497$	8.12224	−	4.20203i	0.364332	−	0.188487i
$498$	2.77710	−	2.12562i	0.124445	−	0.0952511i
$499$	−40.6641	−	9.28132i	−1.82038	−	0.415489i	−0.830452	−	0.557090i	$-0.811918\pi$
$499$	−40.6641	−	9.28132i	−1.82038	−	0.415489i	−0.989924	+	0.141601i	$0.954775\pi$
$500$	−10.0991	−	8.73359i	−0.451647	−	0.390578i
$501$	−0.0195598	−	0.0856972i	−0.000873869	−	0.00382867i
$502$	−5.68816	+	11.2338i	−0.253875	+	0.501391i
$503$	−7.97393	−	34.9361i	−0.355540	−	1.55772i	−0.764165	−	0.645020i	$-0.776849\pi$
$503$	−7.97393	−	34.9361i	−0.355540	−	1.55772i	0.408625	−	0.912702i	$-0.366008\pi$
$504$	9.74733	−	4.32607i	0.434181	−	0.192699i
$505$	−8.48451	+	37.1731i	−0.377556	+	1.65418i
$506$	38.9729	+	32.3699i	1.73256	+	1.43902i
$507$	14.2144	+	6.84532i	0.631286	+	0.304011i
$508$	0.572755	−	14.3768i	0.0254119	−	0.637868i
$509$		−	1.06757i		−	0.0473193i	−0.999720	−	0.0236597i	$-0.992468\pi$
$509$		−	1.06757i		−	0.0473193i	0.999720	−	0.0236597i	$-0.00753181\pi$
$510$	13.2753	−	26.2181i	0.587840	−	1.16096i
$511$	−4.73919	+	23.8982i	−0.209649	+	1.05719i
$512$	−6.02713	−	21.8099i	−0.266364	−	0.963872i
$513$	−5.04265	+	2.42841i	−0.222638	+	0.107217i
$514$	1.16402	−	4.66938i	0.0513427	−	0.205957i
$515$	−8.75553	−	1.99839i	−0.385815	−	0.0880597i
$516$	−1.72169	−	3.97234i	−0.0757933	−	0.174872i
$517$	−5.88921	−	12.2291i	−0.259007	−	0.537834i
$518$	8.53289	−	38.9480i	0.374914	−	1.71128i
$519$	12.0594	−	25.0415i	0.529347	−	1.09920i
$520$	−2.10379	+	35.1818i	−0.0922575	+	1.54282i
$521$		−	27.4146i		−	1.20106i	−0.799603	−	0.600529i	$-0.794957\pi$
$521$		−	27.4146i		−	1.20106i	0.799603	−	0.600529i	$-0.205043\pi$
$522$	2.65517	−	5.24383i	0.116214	−	0.229516i
$523$	4.06277	−	5.09456i	0.177653	−	0.222769i	−0.685030	−	0.728515i	$-0.740211\pi$
$523$	4.06277	−	5.09456i	0.177653	−	0.222769i	0.862683	+	0.505745i	$0.168782\pi$
$524$	−4.97636	+	18.3940i	−0.217393	+	0.803546i
$525$	−6.58346	−	12.7254i	−0.287326	−	0.555380i
$526$	−2.57886	−	12.4348i	−0.112443	−	0.542185i
$527$	3.40259	−	7.06556i	0.148219	−	0.307781i
$528$	−43.0652	+	6.27821i	−1.87417	+	0.273224i
$529$	−15.5705	+	19.5247i	−0.676977	+	0.848902i
$530$	−4.02477	+	16.1450i	−0.174825	+	0.701296i
$531$	−2.15591	−	2.70343i	−0.0935587	−	0.117319i
$532$	3.78830	+	8.09694i	0.164244	+	0.351047i
$533$	−8.85031	+	11.0979i	−0.383349	+	0.480705i
$534$	22.4384	+	29.3156i	0.971003	+	1.26861i
$535$	−15.8047	+	7.61116i	−0.683299	+	0.329059i
$536$	21.6314	+	30.7221i	0.934335	+	1.32699i
$537$	21.4913	−	4.90526i	0.927420	−	0.211678i
$538$	44.6604	+	0.889256i	1.92545	+	0.0383386i
$539$	34.7786	−	10.0634i	1.49802	−	0.433460i
$540$	−0.725916	+	18.2213i	−0.0312384	+	0.784120i
$541$	−7.61056	−	33.3441i	−0.327204	−	1.43357i	−0.824436	−	0.565956i	$-0.808507\pi$
$541$	−7.61056	−	33.3441i	−0.327204	−	1.43357i	0.497232	−	0.867618i	$-0.334350\pi$
$542$	−8.09151	+	6.19331i	−0.347560	+	0.266025i
$543$	6.10799	+	12.6834i	0.262119	+	0.544296i
$544$	11.0193	+	17.0541i	0.472448	+	0.731190i
$545$	2.28281	+	1.82048i	0.0977850	+	0.0779809i
$546$	15.1816	−	32.2414i	0.649714	−	1.37981i
$547$	−23.0956	+	18.4181i	−0.987496	+	0.787502i	−0.977173	−	0.212445i	$-0.931857\pi$
$547$	−23.0956	+	18.4181i	−0.987496	+	0.787502i	−0.0103232	+	0.999947i	$0.503286\pi$
$548$	−4.06321	+	15.0187i	−0.173572	+	0.641569i
$549$	−13.0572	−	10.4128i	−0.557268	−	0.444406i
$550$	3.82377	+	18.4376i	0.163046	+	0.786183i
$551$	4.43911	+	2.13776i	0.189112	+	0.0910717i
$552$	−6.75555	−	40.6526i	−0.287536	−	1.73029i
$553$	−10.5851	+	0.303152i	−0.450125	+	0.0128913i
$554$	1.75267	+	0.436918i	0.0744636	+	0.0185629i
$555$	−48.2332	−	38.4647i	−2.04738	−	1.63273i
$556$	−12.9140	−	6.86524i	−0.547675	−	0.291151i
$557$	36.8155			1.55992			0.779962	−	0.625827i	$-0.215238\pi$
$557$	36.8155			1.55992			0.779962	+	0.625827i	$0.215238\pi$
$558$	0.0876576	−	4.40235i	0.00371084	−	0.186367i
$559$	−4.19783	−	2.02157i	−0.177549	−	0.0855032i
$560$	29.0881	+	1.48490i	1.22920	+	0.0627483i
$561$	35.1850	−	16.9442i	1.48551	−	0.715386i
$562$	−16.7595	−	36.6505i	−0.706957	−	1.54601i
$563$	−9.79198	+	42.9015i	−0.412683	+	1.80808i	0.158617	+	0.987340i	$0.449297\pi$
$563$	−9.79198	+	42.9015i	−0.412683	+	1.80808i	−0.571299	+	0.820742i	$0.693561\pi$
$564$	−2.88335	+	10.6577i	−0.121411	+	0.448768i
$565$	15.2812	+	31.7318i	0.642887	+	1.33497i
$566$	−4.87729	−	10.6659i	−0.205008	−	0.448322i
$567$	12.1354	−	27.1622i	0.509637	−	1.14071i
$568$	8.53918	+	4.75995i	0.358296	+	0.199723i
$569$	−11.4574			−0.480318			−0.240159	−	0.970734i	$-0.577200\pi$
$569$	−11.4574			−0.480318			−0.240159	+	0.970734i	$0.577200\pi$
$570$	13.8289	+	0.275354i	0.579227	+	0.0115333i
$571$	−17.8429	+	37.0512i	−0.746702	+	1.55054i	0.0856683	+	0.996324i	$0.472697\pi$
$571$	−17.8429	+	37.0512i	−0.746702	+	1.55054i	−0.832371	+	0.554220i	$0.813017\pi$
$572$	−30.6363	+	35.4264i	−1.28097	+	1.48125i
$573$	−1.99871	−	0.456193i	−0.0834974	−	0.0190577i
$574$	9.23472	+	7.23357i	0.385450	+	0.301923i
$575$	−17.3833	+	3.96763i	−0.724934	+	0.165461i
$576$	9.60885	+	6.13530i	0.400369	+	0.255638i
$577$	23.7265	−	5.41542i	0.987747	−	0.225447i	0.302017	−	0.953303i	$-0.402340\pi$
$577$	23.7265	−	5.41542i	0.987747	−	0.225447i	0.685730	+	0.727856i	$0.259483\pi$
$578$	4.47847	+	3.71970i	0.186280	+	0.154719i
$579$	4.74282	−	20.7797i	0.197105	−	0.863573i
$580$	12.9394	−	9.50145i	0.537278	−	0.394526i
$581$	−3.05085	−	0.605007i	−0.126571	−	0.0250999i
$582$	−5.66324	+	6.81847i	−0.234749	+	0.282635i
$583$	−17.2875	+	13.7863i	−0.715973	+	0.570970i
$584$	−24.0991	+	9.87993i	−0.997228	+	0.408834i
$585$	−11.0717	−	13.8834i	−0.457756	−	0.574008i
$586$	−6.23215	−	30.0505i	−0.257448	−	1.24137i
$587$	−8.99640			−0.371321			−0.185661	−	0.982614i	$-0.559443\pi$
$587$	−8.99640			−0.371321			−0.185661	+	0.982614i	$0.559443\pi$
$588$	−26.7526	−	12.3131i	−1.10326	−	0.507785i
$589$	3.69103			0.152086
$590$	−1.91777	−	9.24719i	−0.0789533	−	0.380701i
$591$	−17.8701	−	22.4084i	−0.735077	−	0.921758i
$592$	39.7530	−	15.3805i	1.63384	−	0.632134i
$593$	17.2415	−	13.7497i	0.708025	−	0.564631i	−0.201899	−	0.979406i	$-0.564711\pi$
$593$	17.2415	−	13.7497i	0.708025	−	0.564631i	0.909924	+	0.414775i	$0.136140\pi$
$594$	−15.4833	+	18.6417i	−0.635289	+	0.764880i
$595$	−25.3036	+	6.54283i	−1.03735	+	0.268230i
$596$	7.80135	+	10.6241i	0.319556	+	0.435181i
$597$	6.14649	−	26.9295i	0.251559	−	1.10215i
$598$	−34.1166	−	28.3364i	−1.39513	−	1.15876i
$599$	20.4136	−	4.65927i	0.834076	−	0.190372i	0.215904	−	0.976415i	$-0.430730\pi$
$599$	20.4136	−	4.65927i	0.834076	−	0.190372i	0.618173	+	0.786042i	$0.287873\pi$
$600$	7.45756	−	13.3786i	0.304454	−	0.546179i
$601$	2.56199	−	0.584758i	0.104506	−	0.0238528i	−0.169948	−	0.985453i	$-0.554360\pi$
$601$	2.56199	−	0.584758i	0.104506	−	0.0238528i	0.274454	+	0.961600i	$0.411503\pi$
$602$	−1.64029	+	3.48350i	−0.0668532	+	0.141977i
$603$	−18.4563	−	4.21252i	−0.751597	−	0.171547i
$604$	−30.6860	−	26.5368i	−1.24860	−	1.07977i
$605$	−18.8089	+	39.0572i	−0.764692	+	1.58790i
$606$	41.2072	+	0.820498i	1.67393	+	0.0333304i
$607$	−18.5115			−0.751358			−0.375679	−	0.926750i	$-0.622590\pi$
$607$	−18.5115			−0.751358			−0.375679	+	0.926750i	$0.622590\pi$
$608$	−4.98158	+	8.15546i	−0.202030	+	0.330747i
$609$	−15.7150	+	4.06348i	−0.636805	+	0.164661i
$610$	−18.9687	−	41.4818i	−0.768021	−	1.67955i
$611$	5.15538	+	10.7053i	0.208564	+	0.433088i
$612$	−9.87509	−	2.67163i	−0.399177	−	0.107994i
$613$	−5.00080	+	21.9099i	−0.201980	+	0.884933i	0.767749	+	0.640751i	$0.221377\pi$
$613$	−5.00080	+	21.9099i	−0.201980	+	0.884933i	−0.969729	+	0.244183i	$0.921480\pi$
$614$	6.72654	+	14.7100i	0.271461	+	0.593645i
$615$	16.3528	−	7.87512i	0.659411	−	0.317555i
$616$	29.4959	+	25.0613i	1.18842	+	1.00975i
$617$	9.84970	+	4.74337i	0.396534	+	0.190961i	0.621515	−	0.783403i	$-0.286518\pi$
$617$	9.84970	+	4.74337i	0.396534	+	0.190961i	−0.224981	+	0.974363i	$0.572232\pi$
$618$	−0.193255	+	9.70571i	−0.00777387	+	0.390421i
$619$	−0.478977			−0.0192517			−0.00962586	−	0.999954i	$-0.503064\pi$
$619$	−0.478977			−0.0192517			−0.00962586	+	0.999954i	$0.503064\pi$
$620$	5.64509	−	10.6188i	0.226712	−	0.426461i
$621$	−17.9405	−	14.3071i	−0.719927	−	0.574123i
$622$	33.1610	+	8.26664i	1.32963	+	0.331462i
$623$	6.38657	−	32.2053i	0.255872	−	1.29028i
$624$	37.6990	−	5.49590i	1.50917	−	0.220012i
$625$	28.1503	+	13.5565i	1.12601	+	0.542259i
$626$	−0.220853	−	1.06492i	−0.00882707	−	0.0425628i
$627$	14.3705	+	11.4601i	0.573903	+	0.457673i
$628$	−36.0723	−	9.75907i	−1.43944	−	0.389429i
$629$	−29.9040	+	23.8477i	−1.19235	+	0.950869i
$630$	−11.3929	+	9.24928i	−0.453905	+	0.368500i
$631$	19.4128	+	15.4812i	0.772812	+	0.616297i	0.928424	−	0.371521i	$-0.121164\pi$
$631$	19.4128	+	15.4812i	0.772812	+	0.616297i	−0.155613	+	0.987818i	$0.549735\pi$
$632$	−6.51738	−	9.25633i	−0.259247	−	0.368197i
$633$	23.9744	+	49.7834i	0.952897	+	1.97871i
$634$	−15.8778	+	12.1530i	−0.630589	+	0.482658i
$635$	4.40575	+	19.3028i	0.174837	+	0.766010i
$636$	17.9717	+	0.715973i	0.712626	+	0.0283902i
$637$	−30.4449	+	8.80940i	−1.20627	+	0.349041i
$638$	21.3286	+	0.424684i	0.844407	+	0.0168134i
$639$	−4.80213	+	1.09605i	−0.189969	+	0.0433592i
$640$	15.8437	+	26.8046i	0.626278	+	1.05955i
$641$	14.1715	−	6.82465i	0.559742	−	0.269558i	−0.132548	−	0.991177i	$-0.542316\pi$
$641$	14.1715	−	6.82465i	0.559742	−	0.269558i	0.692291	+	0.721619i	$0.256602\pi$
$642$	11.5251	+	15.0574i	0.454858	+	0.594268i
$643$	−18.8208	+	23.6005i	−0.742220	+	0.930714i	−0.999364	−	0.0356591i	$-0.988647\pi$
$643$	−18.8208	+	23.6005i	−0.742220	+	0.930714i	0.257144	+	0.966373i	$0.417218\pi$
$644$	−23.1702	+	28.3970i	−0.913034	+	1.11900i
$645$	3.71449	+	4.65782i	0.146258	+	0.183401i
$646$	2.07427	−	8.32079i	0.0816112	−	0.327377i
$647$	9.63166	−	12.0777i	0.378660	−	0.474824i	−0.555583	−	0.831461i	$-0.687505\pi$
$647$	9.63166	−	12.0777i	0.378660	−	0.474824i	0.934243	+	0.356636i	$0.116076\pi$
$648$	31.3737	−	5.21360i	1.23247	−	0.204810i
$649$	5.44521	−	11.3071i	0.213743	−	0.443842i
$650$	−3.34730	−	16.1402i	−0.131292	−	0.633070i
$651$	−9.28606	+	7.85064i	−0.363949	+	0.307691i
$652$	33.2449	+	8.99416i	1.30197	+	0.352238i
$653$	−26.5214	+	33.2568i	−1.03786	+	1.30144i	−0.0855426	+	0.996335i	$0.527262\pi$
$653$	−26.5214	+	33.2568i	−1.03786	+	1.30144i	−0.952319	+	0.305103i	$0.901309\pi$
$654$	1.42575	−	2.81579i	0.0557512	−	0.110106i
$655$		−	26.2215i		−	1.02456i
$656$	−0.997608	+	12.5007i	−0.0389501	+	0.488070i
$657$	5.69376	−	11.8232i	0.222135	−	0.461268i
$658$	8.80927	−	4.33738i	0.343421	−	0.169089i
$659$	−11.2074	−	23.2724i	−0.436579	−	0.906565i	−0.996929	−	0.0783095i	$-0.975048\pi$
$659$	−11.2074	−	23.2724i	−0.436579	−	0.906565i	0.560350	−	0.828256i	$-0.310667\pi$
$660$	54.9482	−	23.8157i	2.13886	−	0.927024i
$661$	−10.3371	−	2.35938i	−0.402068	−	0.0917694i	0.0167047	−	0.999860i	$-0.494682\pi$
$661$	−10.3371	−	2.35938i	−0.402068	−	0.0917694i	−0.418773	+	0.908091i	$0.637540\pi$
$662$	1.01964	−	4.09023i	0.0396296	−	0.158971i
$663$	−30.8008	+	14.8329i	−1.19620	+	0.576061i
$664$	−1.26128	−	3.07650i	−0.0489470	−	0.119391i
$665$	−7.94184	−	9.39394i	−0.307971	−	0.364281i
$666$	−9.70138	+	19.1598i	−0.375921	+	0.742426i
$667$			20.2003i			0.782160i
$668$	−0.0835065	−	0.00332680i	−0.00323096	−	0.000128718i
$669$	−18.5578	−	8.93696i	−0.717486	−	0.345523i
$670$	−39.7739	−	33.0352i	−1.53660	−	1.27626i
$671$	13.4880	−	59.0947i	0.520697	−	2.28132i
$672$	−4.81336	−	31.1134i	−0.185679	−	1.20023i
$673$	9.95220	+	43.6035i	0.383629	+	1.68079i	0.686002	+	0.727600i	$0.259364\pi$
$673$	9.95220	+	43.6035i	0.383629	+	1.68079i	−0.302372	+	0.953190i	$0.597779\pi$
$674$	−7.88298	+	15.5685i	−0.303641	+	0.599677i
$675$	−1.89782	−	8.31488i	−0.0730470	−	0.320040i
$676$	9.81175	−	11.3459i	0.377375	−	0.436379i
$677$	−8.77794	−	2.00351i	−0.337364	−	0.0770011i	0.0504830	−	0.998725i	$-0.483924\pi$
$677$	−8.77794	−	2.00351i	−0.337364	−	0.0770011i	−0.387847	+	0.921724i	$0.626781\pi$
$678$	30.2314	−	23.1393i	1.16103	−	0.888660i
$679$	7.87966	−	0.225669i	0.302394	−	0.00866038i
$680$	−20.7658	−	18.6934i	−0.796334	−	0.716859i
$681$	−21.9013	−	27.4633i	−0.839259	−	1.05240i
$682$	14.5338	−	6.64597i	0.556527	−	0.254488i
$683$	−5.66188	+	4.51520i	−0.216646	+	0.172769i	−0.725799	−	0.687906i	$-0.758530\pi$
$683$	−5.66188	+	4.51520i	−0.216646	+	0.172769i	0.509154	+	0.860676i	$0.329958\pi$
$684$	−0.883712	−	4.73315i	−0.0337896	−	0.180976i
$685$		−	21.4099i		−	0.818029i
$686$	7.49922	+	25.0951i	0.286322	+	0.958134i
$687$		−	43.7386i		−	1.66873i
$688$	−4.07316	+	0.593800i	−0.155288	+	0.0226384i
$689$	15.1333	−	12.0684i	0.576534	−	0.459771i
$690$	23.5827	+	51.5719i	0.897779	+	1.96331i
$691$	21.9397	+	27.5115i	0.834626	+	1.04659i	0.998195	+	0.0600558i	$0.0191279\pi$
$691$	21.9397	+	27.5115i	0.834626	+	1.04659i	−0.163569	+	0.986532i	$0.552301\pi$
$692$	−19.9879	−	17.2853i	−0.759827	−	0.657089i
$693$	−19.4930	+	0.558269i	−0.740478	+	0.0212069i
$694$	7.60237	+	9.93245i	0.288582	+	0.377030i
$695$	19.6210	+	4.47838i	0.744269	+	0.169874i
$696$	−12.8968	−	11.6097i	−0.488852	−	0.440064i
$697$	−2.50402	−	10.9708i	−0.0948466	−	0.415550i
$698$	16.8529	+	8.53334i	0.637893	+	0.322992i
$699$	6.48918	+	28.4309i	0.245443	+	1.07536i
$700$	−13.3135	+	2.88243i	−0.503204	+	0.108946i
$701$	−9.42493	+	41.2933i	−0.355975	+	1.55963i	0.407141	+	0.913365i	$0.366526\pi$
$701$	−9.42493	+	41.2933i	−0.355975	+	1.55963i	−0.763116	+	0.646262i	$0.776331\pi$
$702$	13.5540	−	16.3189i	0.511563	−	0.615916i
$703$	−16.2195	−	7.81089i	−0.611730	−	0.294593i
$704$	−4.93092	+	41.0826i	−0.185841	+	1.54836i
$705$		−	15.1929i		−	0.572199i
$706$	21.8439	+	11.0605i	0.822105	+	0.416266i
$707$	−23.6651	−	27.9920i	−0.890017	−	1.05275i
$708$	−9.36647	+	4.05962i	−0.352014	+	0.152570i
$709$	31.4308	−	15.1363i	1.18041	−	0.568455i	0.262378	−	0.964965i	$-0.415493\pi$
$709$	31.4308	−	15.1363i	1.18041	−	0.568455i	0.918030	+	0.396510i	$0.129779\pi$
$710$	−13.0533	−	3.25404i	−0.489883	−	0.122122i
$711$	5.56073	+	1.26920i	0.208544	+	0.0475987i
$712$	32.4761	−	13.3143i	1.21709	−	0.498973i
$713$	6.56589	+	13.6342i	0.245895	+	0.510605i
$714$	12.4794	+	25.3457i	0.467028	+	0.948539i
$715$	27.9637	−	58.0673i	1.04578	−	2.17159i
$716$	0.834302	−	20.9419i	0.0311793	−	0.782637i
$717$			20.9413i			0.782066i
$718$	26.9626	+	13.6523i	1.00624	+	0.509499i
$719$	−11.4455	+	14.3522i	−0.426844	+	0.535246i	−0.948023	−	0.318202i	$-0.896921\pi$
$719$	−11.4455	+	14.3522i	−0.426844	+	0.535246i	0.521179	+	0.853448i	$0.325492\pi$
$720$	−14.9684	−	4.69654i	−0.557841	−	0.175030i
$721$	6.59309	−	5.57394i	0.245539	−	0.207584i
$722$	−22.3582	+	4.63684i	−0.832084	+	0.172565i
$723$	−5.34101	+	11.0907i	−0.198634	+	0.412469i
$724$	13.1569	−	2.45649i	0.488974	−	0.0912947i
$725$	−4.68112	+	5.86994i	−0.173853	+	0.218004i
$726$	45.4677	+	11.3345i	1.68746	+	0.420664i
$727$	10.2179	+	12.8128i	0.378960	+	0.475201i	0.934333	−	0.356400i	$-0.115996\pi$
$727$	10.2179	+	12.8128i	0.378960	+	0.475201i	−0.555373	+	0.831601i	$0.687425\pi$
$728$	−25.8205	−	21.9385i	−0.956973	−	0.813096i
$729$	3.04487	−	3.81815i	0.112773	−	0.141413i
$730$	28.4608	−	21.7841i	1.05338	−	0.806266i
$731$	3.32784	−	1.60261i	0.123085	−	0.0592745i
$732$	−39.7415	+	29.1824i	−1.46889	+	1.07861i
$733$	2.85067	−	0.650648i	0.105292	−	0.0240322i	−0.169550	−	0.985522i	$-0.554231\pi$
$733$	2.85067	−	0.650648i	0.105292	−	0.0240322i	0.274842	+	0.961489i	$0.411374\pi$
$734$	−0.292154	+	14.6726i	−0.0107836	+	0.541575i
$735$	39.9609	+	6.74181i	1.47398	+	0.248675i
$736$	−38.9869	−	3.89380i	−1.43708	−	0.143527i
$737$	−15.2891	−	66.9857i	−0.563180	−	2.46745i
$738$	−3.84029	−	5.01731i	−0.141363	−	0.184690i
$739$	8.70837	+	18.0831i	0.320343	+	0.665199i	0.997502	−	0.0706379i	$-0.0225035\pi$
$739$	8.70837	+	18.0831i	0.320343	+	0.665199i	−0.677159	+	0.735836i	$0.736789\pi$
$740$	−47.2775	+	34.7161i	−1.73796	+	1.27619i
$741$	−12.5799	−	10.0321i	−0.462133	−	0.368539i
$742$	−10.0820	−	12.4186i	−0.370121	−	0.455902i
$743$	−2.18383	+	1.74154i	−0.0801168	+	0.0638910i	−0.662729	−	0.748859i	$-0.730602\pi$
$743$	−2.18383	+	1.74154i	−0.0801168	+	0.0638910i	0.582612	+	0.812750i	$0.302031\pi$
$744$	−12.4783	−	3.64400i	−0.457477	−	0.133596i
$745$	−14.1806	−	11.3087i	−0.519539	−	0.414318i
$746$	−13.2605	+	2.75008i	−0.485501	+	0.100688i
$747$	1.50936	+	0.726869i	0.0552245	+	0.0265947i
$748$	−6.81457	−	36.4987i	−0.249165	−	1.33453i
$749$	3.28034	−	16.5417i	0.119861	−	0.604419i
$750$	4.80387	−	19.2704i	0.175412	−	0.703654i
$751$	9.18263	+	7.32290i	0.335079	+	0.267217i	0.776545	−	0.630061i	$-0.216970\pi$
$751$	9.18263	+	7.32290i	0.335079	+	0.267217i	−0.441467	+	0.897278i	$0.645542\pi$
$752$	9.06530	+	5.29246i	0.330577	+	0.192996i
$753$	−18.7298			−0.682553
$754$	−18.6709	−	0.371766i	−0.679954	−	0.0135389i
$755$	50.2973	+	24.2219i	1.83051	+	0.881525i
$756$	−13.5830	−	11.0829i	−0.494009	−	0.403081i
$757$	−20.4941	+	9.86943i	−0.744870	+	0.358711i	−0.767513	−	0.641033i	$-0.778506\pi$
$757$	−20.4941	+	9.86943i	−0.744870	+	0.358711i	0.0226431	+	0.999744i	$0.492792\pi$
$758$	−11.5078	+	5.26229i	−0.417984	+	0.191135i
$759$	−16.7688	+	73.4691i	−0.608670	+	2.66676i
$760$	3.68634	−	12.6233i	0.133717	−	0.457894i
$761$	−15.0105	−	31.1696i	−0.544129	−	1.12990i	−0.973904	−	0.226960i	$-0.927121\pi$
$761$	−15.0105	−	31.1696i	−0.544129	−	1.12990i	0.429775	−	0.902936i	$-0.358593\pi$
$762$	19.4635	−	8.90022i	0.705087	−	0.322421i
$763$	−2.71757	+	0.702691i	−0.0983827	+	0.0254391i
$764$	−0.914946	+	1.72108i	−0.0331016	+	0.0622664i
$765$	14.0774			0.508968
$766$	−0.762219	+	38.2803i	−0.0275401	+	1.38312i
$767$	−4.76670	+	9.89815i	−0.172116	+	0.357402i
$768$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38475 - 0.287182i) q^{2} +(1.31156 + 1.64465i) q^{3} +(1.83505 - 0.795349i) q^{4} +(-2.15171 + 1.71594i) q^{5} +(2.28850 + 1.90077i) q^{6} +(-0.0757418 - 2.64467i) q^{7} +(2.31268 - 1.62835i) q^{8} +(-0.317107 + 1.38934i) q^{9} +O(q^{10})\)	\(q+(1.38475 - 0.287182i) q^{2} +(1.31156 + 1.64465i) q^{3} +(1.83505 - 0.795349i) q^{4} +(-2.15171 + 1.71594i) q^{5} +(2.28850 + 1.90077i) q^{6} +(-0.0757418 - 2.64467i) q^{7} +(2.31268 - 1.62835i) q^{8} +(-0.317107 + 1.38934i) q^{9} +(-2.48680 + 2.99407i) q^{10} +(-5.04250 + 1.15092i) q^{11} +(3.71486 + 1.97487i) q^{12} +(4.41417 - 1.00751i) q^{13} +(-0.864384 - 3.64045i) q^{14} +(-5.64422 - 1.28826i) q^{15} +(2.73484 - 2.91902i) q^{16} +(-1.55736 + 3.23389i) q^{17} +(-0.0401206 + 2.01495i) q^{18} -1.68938 q^{19} +(-2.58374 + 4.86020i) q^{20} +(4.25021 - 3.59322i) q^{21} +(-6.65207 + 3.04185i) q^{22} +(-3.00519 - 6.24035i) q^{23} +(5.71129 + 1.66785i) q^{24} +(0.572838 - 2.50977i) q^{25} +(5.82318 - 2.66281i) q^{26} +(2.98492 - 1.43746i) q^{27} +(-2.24242 - 4.79286i) q^{28} +(-2.62766 - 1.26542i) q^{29} +(-8.18578 - 0.162991i) q^{30} -2.18485 q^{31} +(2.94877 - 4.82750i) q^{32} +(-8.50641 - 6.78364i) q^{33} +(-1.22783 + 4.92536i) q^{34} +(4.70105 + 5.56060i) q^{35} +(0.523100 + 2.80172i) q^{36} +(9.60088 + 4.62354i) q^{37} +(-2.33936 + 0.485158i) q^{38} +(7.44646 + 5.93835i) q^{39} +(-2.18207 + 7.47215i) q^{40} +(-2.45112 + 1.95471i) q^{41} +(4.85356 - 6.19628i) q^{42} +(-0.804546 - 0.641604i) q^{43} +(-8.33787 + 6.12254i) q^{44} +(-1.70169 - 3.53359i) q^{45} +(-5.95355 - 7.77827i) q^{46} +(0.583958 + 2.55849i) q^{47} +(8.38767 + 0.669372i) q^{48} +(-6.98853 + 0.400624i) q^{49} +(0.0724760 - 3.63990i) q^{50} +(-7.36118 + 1.68014i) q^{51} +(7.29892 - 5.35964i) q^{52} +(3.85172 - 1.85489i) q^{53} +(3.72054 - 2.84773i) q^{54} +(8.87512 - 11.1290i) q^{55} +(-4.48162 - 5.99292i) q^{56} +(-2.21572 - 2.77843i) q^{57} +(-4.00205 - 0.997664i) q^{58} +(-1.51285 + 1.89706i) q^{59} +(-11.3821 + 2.12511i) q^{60} +(-5.08482 + 10.5587i) q^{61} +(-3.02547 + 0.627450i) q^{62} +(3.69835 + 0.733411i) q^{63} +(2.69693 - 7.53170i) q^{64} +(-7.76922 + 9.74230i) q^{65} +(-13.7274 - 6.95074i) q^{66} +13.2842i q^{67} +(-0.285764 + 7.17300i) q^{68} +(6.32167 - 13.1271i) q^{69} +(8.10668 + 6.34997i) q^{70} +(1.49968 + 3.11413i) q^{71} +(1.52896 + 3.72944i) q^{72} +(-8.97767 - 2.04910i) q^{73} +(14.6226 + 3.64524i) q^{74} +(4.87900 - 2.34960i) q^{75} +(-3.10009 + 1.34364i) q^{76} +(3.42572 + 13.2486i) q^{77} +(12.0169 + 6.08463i) q^{78} -4.00244i q^{79} +(-0.875748 + 10.9737i) q^{80} +(10.1308 + 4.87876i) q^{81} +(-2.83283 + 3.41069i) q^{82} +(0.261589 - 1.14609i) q^{83} +(4.94149 - 9.97414i) q^{84} +(-2.19815 - 9.63073i) q^{85} +(-1.29835 - 0.657409i) q^{86} +(-1.36518 - 5.98125i) q^{87} +(-9.78756 + 10.8727i) q^{88} +(12.0984 + 2.76138i) q^{89} +(-3.37119 - 4.40444i) q^{90} +(-2.99886 - 11.5977i) q^{91} +(-10.4779 - 9.06119i) q^{92} +(-2.86557 - 3.59331i) q^{93} +(1.54339 + 3.37516i) q^{94} +(3.63505 - 2.89886i) q^{95} +(11.8070 - 1.48188i) q^{96} +2.97945i q^{97} +(-9.56229 + 2.56174i) q^{98} -7.37069i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

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